具有时滞结构的古诺特投资博弈动力学研究

发布时间：2018-03-02 03:04

本文关键词： 古诺特博弈投资有限理性时滞动力系统　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：在传统的古诺特寡头博弈模型中,产量是参与人的决策变量。然而在某些新兴产业的初期,企业可能缺少前期资本积累而不能够完全形成产量博弈。本文针对生产者将投资作为决策变量的博弈竞争问题,在参与人具有有限理性的条件下,建立了两个具有时滞结构的投资博弈动力模型并分析其动力学性质。在构建的第一个模型中,一个参与人仅依据当期的边际利润作出下一个时期的投资决策调整;而另一个参与人则考虑了时滞因素,其决策是利用前期与当期边际利润的加权信息去调整下一个时期的投资策略。经过对模型系统的稳定性的分析,得到了边界均衡是不稳定的结论,并给出了内点均衡局部渐近稳定的条件。利用数值模拟分析了模型参数取值的变化对动力系统的稳定性以及系统的动态复杂行为的重要影响。在第二个模型中,两个参与人都具有时滞决策理性,都依据具有时滞的边际利润的加权信息去调整投资策略。对其对应的离散动力系统,证明了边界均衡不稳定、也给出了内点均衡局部渐近稳定的条件。数值模拟也获得了模型参数大小的改变如何影响系统稳定性的相应结论。本文基于两个动力系统的研究表明,参与人在投资策略的动态调整过程中,较高的调整速度容易导致均衡点不稳定且使得系统出现混沌行为;参与人适当的时滞决策理性会增大系统的稳定性;较小的资本折旧率也能够提高系统的稳定性。数值模拟还表明了,在一定条件下系统可以通过倍周期分岔或者Neimark-Sacker分岔而失去稳定性。
[Abstract]:In the traditional Gunot oligopoly game model, output is the decision variable of the participants. However, in the early stage of some new industries, The enterprise may lack the capital accumulation in the early stage and can not form the production game completely. This paper aims at the competition problem in which the producer takes the investment as the decision variable, under the condition that the participant has the limited rationality, Two dynamic models of investment game with time-delay structure are established and their dynamic properties are analyzed. In the first model, one participant only makes the adjustment of investment decision in the next period according to the marginal profit of the current period. The other participant considers the delay factor, and the decision is to adjust the investment strategy of the next period by using the weighted information of the profit margin in the preceding period and the current period. After the analysis of the stability of the model system, It is concluded that the boundary equilibrium is unstable. The condition of local asymptotic stability of the interior point equilibrium is given. The important influence of the variation of the model parameters on the stability of the dynamic system and the dynamic complex behavior of the dynamic system is analyzed by numerical simulation. In the second model, Both participants have the rationality of time-delay decision-making, and both adjust their investment strategies according to the weighted information of the marginal profit with time delay. For the corresponding discrete dynamical system, it is proved that the boundary equilibrium is unstable. The condition of local asymptotic stability of interior point equilibrium is also given. The numerical simulation also obtains the corresponding conclusion on how the change of model parameters affects the stability of the system. In this paper, based on the study of two dynamical systems, it is shown that the stability of the system is affected by the variation of the model parameters. In the process of dynamic adjustment of investment strategy, the higher adjustment speed leads to instability of equilibrium point and chaotic behavior of the system, and the stability of the system will be enhanced by appropriate delay decision rationality of the participant. The numerical simulation also shows that under certain conditions the system can lose its stability by double period bifurcation or Neimark-Sacker bifurcation.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224.32

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